The hypotenuse of a right angled triangle is 2√13 cm . If the smaller side is increased by 2 cm and the larger side is increased by 3 cm , the new hypotenuse will be √117 cm . Find the length of the larger side of the right angled triangle .
Answers
Statement:
The hypotenuse of a right angled triangle is 2√13 cm. If the smaller side is increased by 2 cm and the larger side is increased by 3 cm, the new hypotenuse will be √117 cm.
To find out:
The length of the larger side of the right angled triangle.
Solution:
Let us consider x as the smaller side and y as the larger side.
Then, in the right angled triangle,
x² + y² = (2√13)² ...(I) [By Pythagoras Theorem]
Now, if the smaller side is increased by 2 cm, then the smaller side will be (x + 2).
And if the larger side is increased by 3 cm, then the larger side will be (y + 3).
Then, in the new right angled triangle,
(x + 2)² + (y + 3)² = (√117)² [By Pythagoras Theorem]
or, x² + 2 × 2 × x + 2² + y² + 2 × 3 × y + 3² = (√117)²
or, x² + 4x + 4 + y² + 6y + 9 = (√117)²
or, x² + y² + 4x + 6y + 13 = (√117)²
Now, put the value of x² + y² from equation (I),
or, (2√13)² + 4x + 6y + 13 = (√117)²
or, (2 × 2 × √13 × √13) + 4x + 6y + 13 = (√117 × √117)
or, 52 + 4x + 6y + 13 = 117
or, 4x + 6y = 117 - 52 - 13
or, 4x + 6y = 52
or, 4x = 52 - 6y
or, x = \( \frac {(52 - 6y)}{4} \) ...(II)
Now, put the value of x of equation (II) in (I),
x² + y² = (2√13)²
or, \( \frac {(2704-624y +36y²)}{16} \) + y² = 52
or, \( \frac {(2704-624y +36y² + 16y²)}{16} \)= 52
or, 52y²-624y + 2704 = 52 × 16
or, 52y² - 624y + 2704 - 832 = 0
or, 52y² - 624y + 1872 = 0
or, 52(y² - 12y + 36) = 0
or, y²-12y +36 = 0 ÷ 52
or, y²-12y +36 = 0
or, (y)² - 2 × 6 × y + (6)² = 0
or, (y - 6)² = 0
or, y - 6=0
or, y = 6
We have taken y as the length of the larger side of the right angled triangle.
So, the length of the larger side is 6 cm.
Answer:
6 cm
Hope you could understand.
If you have any query, feel free to ask.
Related Questions
Give two pairs of polar coordinates for the point (0, -10)
Answers
The required two pairs of polar coordinates for the point (0, -10) are:
(10, π/2) and (10, -π/2)
To convert from Cartesian coordinates (x, y) to polar coordinates (r, θ), we can use the following formulas:
\(r = \sqrt{(x^2 + y^2)}\\\theta = \tan^{-1}(y/x)\)
Since the x-coordinate of the point (0, -10) is 0, we can directly say that the angle θ is either π/2 or -π/2, depending on whether y is positive or negative.
For y = -10, we get:
\(r = \sqrt{(0^2 + (-10)^2)} = 10\)
Therefore, two pairs of polar coordinates for the point (0, -10) are:
(10, π/2) and (10, -π/2)
Both of these pairs have the same distance from the origin (r = 10) but different angles (π/2 and -π/2).
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cost of sweaters
2
4
7
9
Number
Cost ($)
38
76
133
171
The rate of change is what ?
Variable
constant, $38/2 sweaters
constant, $19/sweater
constant, $57/3 sweaters
Answers
Answer:
I would say constant, $19/sweater. The table doesn't go up by 2s or 3s.
Step-by-step explanation:
When z=−6, evaluate −2(z+9)−(−5) and −2⋅z−2⋅9+5 to show that −2(z+9)−(−5)=−2⋅z−2⋅9+5
Answers
Ignore this, I posted the wrong answer and I don't know how to delete it.
Answer:
Yes/true
Step-by-step explanation:
-2(z+9)-(-5)=-2⋅z-2⋅9+5
sostituisco la lettera dandogli un valore
=-2(-6+9)-(-5)=-2⋅(-6)-2⋅9+5
calcolo e tolgo le parentesi
=-2⋅3+5=12-18+5
Elimino i termini uguali
=-2⋅3=12-18
Somma e moltiplicazione tra i numeri
=-6=-6
A baseball player had batting average of 0.298 what the probability of him getting exactly 4 out of 10 times he was up at bat
Answers
The probability of the baseball player getting exactly 4 hits out of 10 times at bat is approximately 0.161, or 16.1%.
To calculate the probability of a baseball player getting exactly 4 hits out of 10 times he was up at bat, we need to use the binomial probability formula.
The binomial probability formula is given by:P(X = k) = C(n, k) * p^k * (1 - p)^(n - k)
Where:
P(X = k) is the probability of getting exactly k hits
n is the total number of trials (in this case, the player's 10 times at bat)
k is the number of successful trials (in this case, 4 hits)
p is the probability of success in a single trial (in this case, the player's batting average, 0.298)
(1 - p) is the probability of failure in a single trial
Plugging in the values:
P(X = 4) = C(10, 4) * (0.298)^4 * (1 - 0.298)^(10 - 4)
Using the combination formula C(n, k) = n! / (k! * (n - k)!):
P(X = 4) = 10! / (4! * (10 - 4)!) * (0.298)^4 * (1 - 0.298)^(10 - 4)
Calculating the values:
P(X = 4) ≈ 0.161
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3.
The Moy family budgeted $32,650 to remodel their kitchen. They spent
$43,987. How much more or less is the amount spent than the amount
budgeted?
A $11,337 more
B $11,337 less
C $17,887 more
D $17,887 less
Answers
Answer:
A
Step-by-step explanation:
43987-32650= 11337
And it’s more
please help with this question
Answers
The probability of the sample mean being less than 25.3 is given as follows:
0.9713 = 97.13%.
The sample mean would not be considered unusual, as it has a probability that is greater than 5%.
How to obtain probabilities using the normal distribution?The z-score of a measure X of a normally distributed variable that has mean represented by \(\mu\) and standard deviation represented by \(\sigma\) is obtained by the equation presented as follows:
\(Z = \frac{X - \mu}{\sigma}\)
The z-score represents how many standard deviations the measure X is above or below the mean of the distribution of the data-set, depending if the obtained z-score is positive(above the mean) or negative(below the mean).The z-score table is used to obtain the p-value of the z-score, and it represents the percentile of the measure X in the distribution.By the Central Limit Theorem, the sampling distribution of sample means of size n has standard deviation given by the equation presented as follows: \(s = \frac{\sigma}{\sqrt{n}}\).The parameters for this problem are given as follows:
\(\mu = 25, \sigma = 1.3, n = 68, s = \frac{1.3}{\sqrt{68}} = 0.1576\)
The probability of a score less than 25.3 is the p-value of Z when X = 25.3, hence:
Z = (25.3 - 25)/0.1576
Z = 1.9
Z = 1.9 has a p-value of 0.9713.
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Pls help with this it’s due soon i need answers pls and thank you
Answers
Based on the given triangle, we can find that:
The length of PN is 11The length of GN 37The size of angle ∠GLN is 32First, we will focus on the triangle NLP. NLP is a right triangle, then we can use the formula of sinus to find the length of NP, where:
Sin ∠NLP = NP / LP
Sin 35° = NP / 20
0.57 = NP / 20
NP = 11.47
NP ≈ 11
Next, we will focus on triangle GLP. GLP is a right triangle with hypotenuse of 52 and the base of 20. Using the Phytagoras theorem we can try to find the triangle's height.
GL² = GP² + LP²
52² = GP² + 20²
2704 = GP² + 400
GP² = 2304
GP = 48
GP = GN + NP
48 = GN + 11
GN = 37
To find the size of angle ∠GLN, we have to find the size of angle ∠PGN first. We will use the Sines Law:
LP / sin ∠PGN = GL / sin ∠GPN
20 / sin ∠PGN = 52 / 1
sin ∠PGN = 20/52
∠PGN = 22.5°
∠PGN ≈ 23°
∠GLP + ∠GPL + ∠PGN = 180°
∠GLP + 90° + 23° = 180°
∠GLP = 67°
∠GLP = ∠GLN + ∠NLP
67° = ∠GLN + 35°
∠GLN = 32°
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When testing whether the correlation coefficient differs from zero, the value of the test statistic is t20 = 1.95 with a corresponding p-value of 0.0653. At the 5% significance level (p = 0.05), can you conclude that the correlation coefficient differs from zero?
a) No, since the p-value exceeds 0.05. b) Yes, since the test statistic value of 1.95 exceeds 0.05. c) No, since the test statistic value of 1.95 exceeds 0.05. d) Yes, since the p-value exceeds 0.05.
Answers
No, we can't conclude that the correlation coefficient differs from zero because the p-value, which is 0.0653 exceeds 0.05. The correct option is a.
Given that:
p-value = 0.0653
Level of significance (p) = 0.05
The null hypothesis is a typical statical theory that suggests that no statical relationship and significance exists in a set of given single observed variables, between two sets of observed data and measured phenomena.
The null hypothesis is significant because it offers a rough description of the phenomena inferred from the available evidence. It enables researchers to empirically test the relationship statement in a study.
Example: The null hypothesis is that the population density is the same across all states.
The hypothesis is
H0: p=0 vs HA: p \(\neq\) 0
We observe that,
p-value > p (level of significance)
So, fail to reject the null hypothesis (H0).
The correlation coefficient differs from zero when the p-value is less than 0.05.
Therefore, we can not conclude that the correlation coefficient differs from zero.
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Cooper invested $3,100 in an account paying an interest rate of 2%
compounded quarterly. Robert invested $3,100 in an account paying an
interest rate of 3 % compounded continuously.After 12 years, how much
more money would Robert have in his account than Cooper, to the nearest
dollar?
Answers
Answer:
Robert will have $481 more in his account than Cooper.
Step-by-step explanation:
Compound interest:
The compound interest formula is given by:
\(A(t) = P(1 + \frac{r}{n})^{nt}\)
Where A(t) is the amount of money after t years, P is the principal(the initial sum of money), r is the interest rate(as a decimal value), n is the number of times that interest is compounded per year and t is the time in years for which the money is invested or borrowed.
Continuous compounding:
Similar to compound interest:
\(A(t) = P(1 + r)^t\)
Cooper:
Cooper invested $3,100 in an account paying an interest rate of 2% compounded quarterly. This means that \(P = 3100, r = 0.02, n = 4\)
After 12 years is A(12). So
\(A(t) = P(1 + \frac{r}{n})^{nt}\)
\(A(12) = 3100(1 + \frac{0.02}{4})^{4*12}\)
\(A(12) = 3938.5\)
Cooper will have $3938.5 in his account.
Robert:
Robert invested $3,100 in an account paying an interest rate of 3 % compounded continuously. So \(P = 3100, r = 0.03\).
After 12 years.
\(A(t) = P(1 + r)^t\)
\(A(12) = 3100(1 + 0.03)^{12}\)
\(A(12) = 4419.9\)
Robert will have $4419.9 in his account.
How much more money would Robert have in his account than Cooper, to the nearest dollar?
4419.9 - 3938.5 = 481.4
To the nearest dollar, Robert will have $481 more in his account than Cooper.
Chandler wants to buy a bike
that costs $345. He has a job that
pays an hourly wage of $6. He
needs to pay back $35 that he
borrowed from his mom. How
many hours does Chandler need to
work to have enough money to
purchase the bike?
Answers
We can divide 345 by 6 to see the remaining hours.
345/6 = 57.5.
Chandler would need to work for 57.5 hours after paying off the debt owed to be able to afford the bike, working for a grand total of 63.5 hours.
Not sure if they would pay for a half an hour of work, so Chandler may need to work 64 hours, unless it’s stated they’d pay for a partial hour of work.
Hope this helps!
A square of an even number is always even.
True or false?
Answers
Answer:
Mostly likely it's True
Step-by-step explanation:
Answer:
True
Step-by-step explanation:
The square of an even number is always even.
Examples:
8² = 64
64² = 4096
6² = 36
13040² = 170,041,600
SOMEONE ANYONE PLEASE HELP!!!
Answers
The graph of g(x) is obtained from the graph of f(x) by the following transformations:
- A horizontal stretch by a factor of 9. This is because the graph of g(x) is 9 times wider than the graph of f(x).
- A vertical translation down by 2 units. This is because the graph of g(x) is 2 units lower than the graph of f(x).
In other words, to obtain the graph of g(x) from the graph of f(x), we stretch the graph horizontally by a factor of 9 and then translate it down by 2 units.
Here is a more detailed explanation of the transformations:
- Horizontal stretch by a factor of 9: To stretch the graph horizontally by a factor of 9, we multiply all of the x-coordinates by 9. This means that every point on the graph of f(x) will be moved 9 units to the right on the graph of g(x).
- Vertical translation down by 2 units: To translate the graph down by 2 units, we subtract 2 from all of the y-coordinates. This means that every point on the graph of f(x) will be moved 2 units down on the graph of g(x).
A teacher surveyed her students about the amount of time the students
studied for a test and plotted it with their corresponding scores. The data
is shown on the scatterplot below.
A
8.
What does the y-intercept of the best-fit linear model represent?
A student who studied for 48 minutes would expect a score of about
58 on the test.
A student who studied for 0 minutes would expect a score of about 48
on the test.
C. A student who studied for 44 minutes would expect a score of about
52 on the test.
D. A student who studied for 0 minutes would expect a score of about 44
on the test.
Review IF 6:10.7 Rate of Change in Context
Samantholimonadanthacown Sha.cocondrathambar
Answers
Answer:
c
Step-by-step explanation:
I just had the exact same question on a worksheet
The brain volumes (cm³) of 20 brains have a mean of 1085.2 cm³ and a standard deviation of 125.6 cm³. Use the
given standard deviation and the range rule of thumb to identify the limits separating values that are significantly low or
significantly high. For such data, would a brain volume of 1386.4 cm³ be significantly high?
Answers
If the brain volumes (cm³) of 20 brains have a mean of 1085.2 cm³ and a standard deviation of 125.6 cm³. For such data: it is significantly low for a brain because 1386.4 cm³ is less than the upper limit.
How to find the lower and upper limits?Mean = 1085.2 cm³
Standard deviation = 125.6 cm³
Hence,
Lower limit = Mean - 2 x Standard deviation
Lower limit =1085.2 - 2 x 125.6
Lower limit =1161.2 - 251.2
Lower limit =910
Upper Limit = Mean + 2 x Standard deviation
Upper Limit = 1161.2 + 2 x 125.6
Upper Limit =1161.2 +251.2
Upper Limit =1412.4
The limit of values is from 910 to 1412.4.
A value below 910 will be is considered low and a value above 1412.4 will be considered high
Therefore 1386.4 cm³ is less than the upper limit. Thus it is significantly low for a brain.
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Daily Dose of MEMES.
#001
Bubble wrap: *exist*
Every single kid in a 12ft distance
Answers
Answer:
lol
Step-by-step explanation:
Answer:
one there is no milk in the fridge but you already poured the cereal
Use the given conditions to write an equation for the line in the indicated form.
Passing through (2, 2) and perpendicular to the line whose equation is y = 4x + 7;
point-slope form
A)y=-4x-10
B)y-2=-1/4(x-2)
C)y-2=1/4(x+2)
D)y-2=1/4(x-2)
Answers
Answer:
B) y - 2 = (-1/4)(x - 2)
Step-by-step explanation:
Start with the equation of the given line: y = 4x + 7.
Determine the slope of the given line, which is 4.
Since the perpendicular line has a negative reciprocal slope, the perpendicular line's slope is -1/4.
Use the point-slope form of a linear equation: y - y₁ = m(x - x₁), where (x₁, y₁) is the given point and m is the slope.
Substitute the values x₁ = 2 and y₁ = 2 into the point-slope equation: y - 2 = (-1/4)(x - 2).
Simplify by distributing -1/4 to (x - 2): y - 2 = (-1/4)x + 1/2.
Add 2 to both sides to isolate y: y = (-1/4)x + 1/2 + 2.
Simplify further: y = (-1/4)x + 5/2.
The equation in point-slope form for the line passing through (2, 2) and perpendicular to y = 4x + 7 is y - 2 = (-1/4)(x - 2), which matches option B.
In a class of students, the following data table summarizes how many students play an instrument or a sport. What is the probability that a student chosen randomly from the class plays a sport or an instrument?
Answers
Answer:
57.14%
Step-by-step explanation:
add those 3 together and convert whats left into a percentage
Dana's phone has zero battery. After charging her phone for 1 minute, it has
2% battery. After 2 minutes, her phone has 6% battery. Based on this, predict
the number of minutes it will take for Dana to charge her phone's battery so
that it has 50% power and 90% power.
Answers
From the first two inference, it takes her phone 1 minute to charge 2% i.e 1 minute of charge = 2% of battery.
Therefore; charging from scratch,
1 min = 2%
x mins = 50%.
using cross multiplication,
x mins = (50% × 1 min) ÷ 2%.
x = 25 mins.
For 90%, applying the same formula,
y min = (90% × 1 min) ÷ 2%
y = 45 mins.
So from zero percent, it will take Dana's phone 25 minutes to charge to 50% and 45 minutes to charge to 90%.
carmela has a deck of 26 alphabet cards. she mixes the cards, places them face down on the table, and turns them over one at a time. what is the probability that the first two cards she turns over are vowel cards (a, e, i, o, u)? 5
Answers
The probability that the first two cards Carmela turns over are vowel cards is 2/65.
To calculate the probability of Carmela turning over two vowel cards (A, E, I, O, U) in a row, we'll need to find the probability of each event and then multiply those probabilities.
Step 1: Calculate the probability of the first card being a vowel.
There are 5 vowel cards (A, E, I, O, U) in a deck of 26 alphabet cards.
So, the probability of the first card being a vowel is 5/26.
Step 2: Calculate the probability of the second card being a vowel.
Since the first card was a vowel, there are now 4 vowel cards left and a total of 25 cards left in the deck. So, the probability of the second card being a vowel is 4/25.
Step 3: Multiply the probabilities of each event.
Now, we multiply the probabilities from Step 1 and Step 2:
(5/26) * (4/25) = 20/650
Step 4: Simplify the fraction.
The fraction can be simplified by dividing both the numerator and denominator by 10:
20/650 = 2/65.
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Solve this system for m and b 342=23m+b 147=10m+b
Answers
Answer:
b = − 3
m = 5 ( 39 + 2 m ) /23
2.m= 147-b/10
What is the predicted house size (in hundreds of square feet) for an individual earning an annual income of 60 (which is measured in thousands of dollars), having a family size of 3, and having 13 years of education
Answers
Full question attached
Answer and explanation:
From the question, we can see that
Twenty-five points are chosen in the plane so that no three of them are collinear. How many triangles do they determine?
Answers
The 25 points determine a total of 2300 triangles when no three points are collinear.
To determine the number of triangles that can be formed using 25 points in the plane, we can use the concept of combinations.
In general, for any given set of n points, the number of triangles that can be formed using these points is given by the formula:
Number of triangles = nC3 = n! / (3! * (n-3)!)
In this case, we have 25 points. Substituting n = 25 into the formula, we get:
Number of triangles = 25C3 = 25! / (3! * (25-3)!)
Simplifying the equation, we have:
Number of triangles = 25! / (3! * 22!)
Since 3! = 3 * 2 * 1 = 6, we can further simplify the equation:
Number of triangles = 25 * 24 * 23 / 6 = 2300
Therefore, the 25 points determine a total of 2300 triangles.
It's important to note that this calculation assumes that no three points are collinear, meaning that no three points lie on the same straight line.
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in the figure, OA/OC=OB/OD=1/4. the value of DC is 120 by the SAS test
Answers
The value of DC is of 80, hence the statement is false.
What are similar triangles?Similar triangles share these two features listed as follows:
Congruent angles, that is, angles that have the same measure.Proportional side lengths.The similar triangles for this problem are given as follows:
AOB and COD.
Hence the proportional relationship established between the side lengths is given as follows:
OA/OC = OB/OD = 1/4 = AB/DC.
Taking the last two terms, considering that AB = 20 cm, the length of DC is given as follows:
DC = 4 x AB
DC = 4 x 20 cm
DC = 80 cm.
Hence the statement is false, as the length is of 80 cm and not of 120 cm.
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write an equation that is perpendicular and passes through two points. y= -1/5x +9. points are 2, -2
Answers
step 1
Find the slope of the given equation
we have
y= -1/5x +9
the slope is -1/5
step 2
Find the slope of the perpendicular line to the given equation
Remember that
If two lines are perpendicular, then their slopes are opposite reciprocal
so
the slope of the perpendicular line is m=5
step 3
Find the equation of the line in slope intercept form
y=mx+b
we have
m=5
point (2,-2)
substitute
-2=5(2)+b
solve for b
-2=10+b
b=-12
therefore
the equation is
y=5x-12hiii can someone help me with this i’m not really good at math and i need some help with this question please
Answers
Answer:
√128 units
Step-by-step explanation:
As we move to the right from (-4, -2) to (4, 6), x increases by 8 and y increases by 8 also. Using the distance formula, we get:
d = √(8² + 8²) = √(64 + 64) = √128 units (last answer)
use the shell method to find the volume of the solid generated by revolving the regions bounded by the curves and lines about the y axis.
y=x2 , y=8-7x , x=0 , for x0
Answers
The volume of the solid generated by revolving the regions bounded by the curves and lines about the y axis is \(\frac{17 \pi}{6}\).
We want the volume generated when the area bounded by the curves:
\($y=x^2, y=8-7 x$\), and x=0 for \(x \geq 0$\) is revolved about the y axis using the cylindrical shell method. The intersection of \($y=x^2$\) and \($y=8-7 x$\) is :
\($$\begin{aligned}& y=x^2=8-7 x \\& x^2+7 x-8=0 \\& (x+8)(x-1)=0 \Rightarrow x=-8 \text { or } x=1 .\end{aligned}\)
We thus have for \($x \geq 0$\) the two curves intersect at x=1 and\($y=1^2=1$\).
The limits for integration are .
The upper curve is \($y_2=8-7 x$\), and the lower curve is\($\cdots y_1=x^2$\).
The height of the shell is \($\cdots h=y_2-y_1=8-7 x-x^2$\).
The radius of the shell is\($\cdots R=x$\).
The surface area of the shell is:
\($$A=2 \pi R h=2 \pi x\left(8-7 x-x^2\right)=2 \pi\left(8 x-7 x^2-x^3\right)$$\)The differential of volume which is the cylindrical shell is :
\($$\mathrm{dv}=\mathrm{Adx}=2 \pi\left(8 x-7 x^2-x^3\right) \mathrm{dx}$$\)We then have the volume of revolution is:
\($$\begin{aligned}& v=2 \pi \int_0^1\left(8 x-7 x^2-x^3\right) d x \\& =2 \pi\left(4 x^2-\frac{7}{3} x^3-\frac{1}{4} x^4\right)_0^1 \\& =2 \pi\left[4\left(1^2-0^2\right)-\frac{7}{3}\left(1^3-0^3\right)-\frac{1}{4}\left(1^4-0^4\right)\right] \\& =2 \pi\left(4-\frac{7}{3}-\frac{1}{4}\right) \\& =2 \pi\left(\frac{48-28-3}{12}\right) \\& =2 \pi\left(\frac{17}{12}\right) \text {; or, we have: } \\& v=\frac{17 \pi}{6} \text {. }\end{aligned}$$\)
Therefore, the volume of the solid generated by revolving the regions bounded by the curves and lines about the y axis is \(\frac{17 \pi}{6}\).
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I have provided a picture
Answers
The regression equation is y = 28.0 + 0.0510x.
The best predicted temperature at a time when the cricket chirps 3000 times in 1 minute, based on the regression equation is 181°F.
What is wrong with this predicted temperature: B. It is unrealistically high. The value 3000 is far outside of the range of observed values.
How to determine the line of best fit?In this scenario, the chirps in 1 min would be plotted on the x-axis (x-coordinate) of the scatter plot while the temperature would be plotted on the y-axis (y-coordinate) of the scatter plot through the use of Microsoft Excel.
From the scatter plot (see attachment) which models the relationship between the chirps in 1 min and the temperature, a regression equation or an equation for the line of best fit is given by:
y = 28.0 + 0.0510x
When x = 3000, the temperature can be calculated as follows;
y = 28.0 + 0.0510(3000)
y = 181°F
In conclusion, a temperature of 181°F is unrealistically too high because a chirps of 3000 times in 1 min is an outlier.
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true or false, \(\pi\) only used to determine the area of a circle?
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In western Kansas, the summer density of hailstorms is estimated at about 1.5 storms per 5 square miles. In most cases, a hailstorm damages only a relatively small area in a square mile. A crop insurance company has insured a tract of 9 square miles of Kansas wheat land against hail damage. Let r be a random variable that represents the number of hailstorms this summer in the 9-square-mile tract.(a) Explain why a Poisson probability distribution is appropriate for r.Hail storms in western Kansas are a common occurrence. It is reasonable to assume the events are dependent.Hail storms in western Kansas are a rare occurrence. It is reasonable to assume the events are dependent. Hail storms in western Kansas are a common occurrence. It is reasonable to assume the events are independent.Hail storms in western Kansas are a rare occurrence. It is reasonable to assume the events are independent.What is λ for the 9-square-mile tract of land? Round λ to the nearest tenth (b) If there already have been two hailstorms this summer, what is the probability that there will be a total of four or more hailstorms in this tract of land? Compute P(r≥ 4 | r ≥ 2). (Use 4 decimal places.)(c) If there already have been three hailstorms this summer, what is the probability that there will be a total of fewer than six hailstorms? Compute P(r < 6 | r ≥ 3). (Use 4 decimal places.)
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Answer:
Step-by-step explanation:
(a) Hail storms in western Kansas are a rare occurrence. It is reasonable to assume the events are independent
(b) The required \(\lambda\) = 1.7 * 10/5 = 3.4
(c) P(r ≥ 4 | r ≥ 2)
= P(r ≥ 4)/P(r ≥ 2)
= {1 - P(r < 4)}/{1 - P(r < 2)}
For Poisson distribution, P(X = x)
\(= \frac{e^{- \lambda} \lambda ^x}{x !}\)
Thus, P(r < 4) = P(r = 0) + P(r = 1) + P(r = 2) + P(r = 3)
= 0.5584
and P(r < 2) = P(r = 0) + P(r = 1) = 0.1468
Thus, P(r ≥ 4 | r ≥ 2) = (1 - 0.5584)/(1 - 0.1468)
= 0.5177
(d) P(r < 6 | r ≥ 3)
= P(3 ≤ r < 6)/P(r ≥ 3)
P(3 ≤ r < 6) = P(r = 3) + P(r = 4) + P(r = 5) = 0.5308
P(r ≥ 3) = 1 - {P(r = 0) + P(r = 1) + P(r = 2)}
= 0.6603
Thus, P(r < 6 | r ≥ 3) = 0.5308/0.6603 = 0.8309
Which ordered pair is a solution of the equation shown? A.-3/4,- 1/2 B. 0,3/4 C.4/3, 1/2 D. 4, 3/2
pls hurry = 50 point
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Answer:
the answer is b, c, d, a, respectively